The first one in my reference book is Megiddo in 1469 BC. That's well over a thousand years before Alexander the Great. It is near the plain of Esdraelon, Israel.
Addition:
We have fragmentary written records of battles in Mesopotamia - eg
- about 2700 BCE the King of Sumer and Akkad 'carried away as spoil the weapons of Elam'.
- about 2550 BCE a battle between Umma and Lagash.